optcrit {OptimalDesign}

Criterion value of a design

Description

Computes the criterion value of a design w in the model determined by the matrix Fx of all regressors.

Usage

optcrit(Fx, w, crit="D", h=NULL, echo=TRUE)

Arguments

Fx

the n times m (where m>=2, m<=n) matrix containing all candidate regressors (as rows), i.e., n is the number of candidate design points, and m (where m>=2) is the number of parameters.

w

a non-negative vector of length n representing the design.

crit

the criterion; possible values are "D", "A", "I", "C" and "c".

h

a non-zero vector of length m corresponding to the coefficients of the linear parameter combination of interest. If crit is not "C" nor "c" then h is ignored. If crit is "C" or "c" and h=NULL then h is assumed to be c(0,...,0,1).

echo

Print the call of the function?

Details

The package works with optimality criteria as information functions, i.e., the criteria are concave, positive homogeneous and upper semicontinuous on the set of all non-negative definite matrices. The criteria are normalized such that they assign the value of 1 to any design with information matrix equal to the identity matrix.

Value

A non-negative number corresponding to the criterion value.

Note

Since the criteria are positive homogeneous, the relative efficiency of two designs is just the ratio of their criterion values.

Author(s)

Radoslav Harman, Lenka Filova

See Also

infmat

Examples

# The Fx matrix for the spring balance weighing model with 6 weighed items.
Fx <- Fx_cube(~x1 + x2 + x3 + x4 + x5 + x6 - 1, lower = rep(0, 6), n.levels = rep(2, 6))

# Criteria of the design of size 15 that weighs each pair of items exactly once.
w2 <- rep(0, 64); w2[apply(Fx, 1, sum) == 2] <- 1
optcrit(Fx, w2, crit = "D")
optcrit(Fx, w2, crit = "A")
optcrit(Fx, w2, crit = "I")

# Criteria for the design of size 15 that weighs each quadruple of items exactly once.
w4 <- rep(0, 64); w4[apply(Fx, 1, sum) == 4] <- 1
optcrit(Fx, w4, crit = "D")
optcrit(Fx, w4, crit = "A")
optcrit(Fx, w4, crit = "I")